The interesting observation is that both 24.305 grams of magnesium and 342 grams of sucrose have the same number of particles. The number of magnesium atoms in 24.305 grams of magnesium is the same as the number of sucrose molecules in 342 grams of sucrose. That number is 6.022 x 1023.

This number is special, it is called Avogadro's number and it is a fundamental unit in the SI system. Specifically this number is called a mol and is defined as the number of 12C atoms in 12 g of 12C. This number has been experimentally determined as 6.022 x 1023 atoms. A mol of any substance is defined as the amount of the substance which contains the same number of units as are in 12 g of 12C or 6.023 x 1023 units of the substance.

So a mol is several things; it is an amount of substance which contains the same number of atoms, molecules or formula units as 12 grams of 12C. We saw earlier than 24.305 grams of magnesium and 342 grams of sucrose contain the same number particles. In the case of magnesium it is atoms, in the case of sucrose it is molecules. But whichever...atoms or molecules...the number is the same. Therefore we refer to 24.305 grams of magnesium as one mol of magnesium. Similarly 342 grams of sucrose is one mol.

How many grams of chlorine, Cl2, are in one mol?

This can be determined by finding the molecular mass of Cl2.

2 x 35.453 u = 70.906 u

The molecular mass of Cl2 is 70.906 u. When this mass is expressed in units of grams, 70.906 grams, that mass of chlorine contains 6.022 x 1023 molecules of Cl2 and is also a mol. So there are 70.9 grams in one mol of Cl2.

A mol of 12C atoms contains 6.023 x 1023 atoms of 12C.

A mol of Cl2 molecules contains 6.023 x 1023 molecules of Cl2.

A mol of MgCl2 contains 6.023 x 1023 formula units of MgCl2.

A mol of 12C atoms weighs the same in grams as the atomic mass of 12C, 12 g. The weight of any substance which contains 6.023 x 1023 units is given by its atomic, molecular or formula mass expressed in grams and is called the molar mass of the substance.

A mol of 12C atoms has a mass 12 g: the molar mass of 12C is 12 g.

A mol of Cl2 molecules has a mass 70.90 g: the molar mass of Cl2 is 70.90 g.

A mol of MgCl2 has a mass 95.2 g: the molar mass of MgCl2 is 95.2 g.

Sample Problem:

Determine the number of moles of N2O5 in 45.6 g of N2O5 gas and the number of nitrogen atoms.

Solution:

The molar mass of N2O5 is 108 g­mol-1. The sample is 45.6 g so we know there is less than a mol since a mol of N2O5 weighs 108 g. To calculate the number of moles we setup the problem in the following way;

To determine the number of nitrogen atoms in the sample we must first determine how many N2O5 molecules.

Now we can determine the number of nitrogen atoms;

Here is one of my favorite problems;